fix(apigateway): allow using GENERATE_IF_NEEDED for the physical name in LambdaRestApi (#19638)

Fixes #9374

----

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Author: skinny85

packages/@aws-cdk/aws-apigateway/lib/restapi.ts

@@ -322,8 +322,11 @@ export abstract class RestApiBase extends Resource implements IRestApi {
   protected cloudWatchAccount?: CfnAccount;
 
   constructor(scope: Construct, id: string, props: RestApiBaseProps = { }) {
-    super(scope, id);
-    this.restApiName = props.restApiName ?? id;
+    const restApiName = props.restApiName ?? id;
+    super(scope, id, {
+      physicalName: restApiName,
+    });
+    this.restApiName = restApiName;
 
     Object.defineProperty(this, RESTAPI_SYMBOL, { value: true });
   }
@@ -736,7 +739,7 @@ export class RestApi extends RestApiBase {
     super(scope, id, props);
 
     const resource = new CfnRestApi(this, 'Resource', {
-      name: this.restApiName,
+      name: this.physicalName,
       description: props.description,
       policy: props.policy,
       failOnWarnings: props.failOnWarnings,

packages/@aws-cdk/aws-apigateway/test/lambda-api.test.ts

@@ -242,4 +242,24 @@ describe('lambda api', () => {
       ],
     });
   });
+
+  test('LambdaRestApi allows passing GENERATE_IF_NEEDED as the physical name', () => {
+    // GIVEN
+    const stack = new cdk.Stack();
+
+    // WHEN
+    new apigw.LambdaRestApi(stack, 'lambda-rest-api', {
+      handler: new lambda.Function(stack, 'handler', {
+        handler: 'index.handler',
+        code: lambda.Code.fromInline('boom'),
+        runtime: lambda.Runtime.NODEJS_10_X,
+      }),
+      restApiName: cdk.PhysicalName.GENERATE_IF_NEEDED,
+    });
+
+    // THEN
+    Template.fromStack(stack).hasResourceProperties('AWS::ApiGateway::RestApi', {
+      Name: Match.absent(),
+    });
+  });
 });